Nonlnear dynamics of ordinary differential equations and applications

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Publications

Generalized synchronization in a system of several non-autonomous oscillators coupled by a medium

Publication . Martins, Rogério; Morais, Gonçalo

An abstract theory on general synchronization of a system of several oscillators coupled by a medium is given. By generalized synchronization we mean the existence of an invariant manifold that allows a reduction in dimension. The case of a concrete system modeling the dynamics of a chemical solution on two containers connected to a third container is studied from the basics to arbitrary perturbations. Conditions under which synchronization occurs are given. Our theoretical results are complemented with a numerical study.

2015Journal article

Open access

Bounded domains of negative multipliers

Publication . Johnson, Charles; Morais, Gonçalo

A natural problem associated with coupling of non-autonomous oscillators and synchronization is described. It leads to a question about the boundedness of a domain associated with a derived quadratic form. Properties of real symmetric matrices with bounded domains are developed, and unboundedness is translated into satisfiability of a certain Lyapunov-like matrix form. Eventually the real symmetric matrices associated with unbounded domains are explicitly characterized in terms of inertia explicit matrices. A consequence of the characterization is that large, irreducible matrices are likely to have bounded domains.

2019-11-01Journal article

Restricted access